Departmental Colloquium
by Rui Loja Fernandes (Illinois Urbana-Champaign)
A classical and important problem, dating back to Poincaré, is to determine whether a periodic orbit of a vector field persists under perturbations of the field. When it does, we say the orbit is stable under perturbations. Analogous questions arise in other settings: does an orbit of a group action persist under perturbations? Does a leaf of a foliation persist under perturbations? In this lecture, I will review classical results addressing these questions and present a “universal stability theorem” from which many of them follow.
